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The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
In this paper, we develop a framework for information theoretic learning based on infinitely divisible matrices. We formulate an entropy-like functional on positive definite matrices based on Renyi's axiomatic definition of entropy and…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.
We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs.
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence,…
In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…
In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions originally considered by Dales and Davie. For many compact plane sets the classical…
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of…
We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…